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Thread: Factoring

  1. #1
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    Factoring

    Can someone show me why

    (a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)
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  2. #2
    Senior Member eumyang's Avatar
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    Use the difference of two squares pattern:
    $\displaystyle x^2 - y^2 = (x - y)(x + y)$

    Substitute "a - b" for x and "c + d" for y:
    $\displaystyle \begin{aligned}
    (a - b)^2 - (c + d)^2 &= [(a - b) - (c + d)][(a - b) + (c + d)] \\
    &= (a - b - c - d)(a - b + c + d)
    \end{aligned}$
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  3. #3
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    Quote Originally Posted by Alan306090 View Post
    Can someone show me why

    (a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)
    let $\displaystyle (a-b) = x$ and $\displaystyle (c+d) = y$

    working from the right side ...

    $\displaystyle (a-b-c-d)(a-b+c+d) =$

    $\displaystyle [(a-b)-(c+d)][(a-b)+(c+d)] =$

    $\displaystyle [x-y][x+y] = $

    $\displaystyle x^2-y^2 =$

    $\displaystyle (a-b)^2 - (c+d)^2$
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